Repeat Problem 10 with an interest rate of 0.5%. For Problems 7–10, formulate a dynamical system that models change exactly for the described situation.

Data from problem 10

Your grandparents have an annuity. The value of the annuity increases each month by an automatic deposit of 1% interest on the previous month's balance. Your grandparents withdraw $1000 at the beginning of each month for living expenses. Currently, they have $50,000 in the annuity. Model the annuity with a dynamical system. Will the annuity run out of money? When? Hint: What value will and a_n  have when the annuity is
depleted?